Abstract
In this paper, we study zero-knowledge (ZK) proofs for circuit satisfiability that can prove to n verifiers at a time efficiently. The proofs are secure against the collusion of a prover and a subset of t verifiers. We refer to such ZK proofs as multi-verifier zero-knowledge (MVZK) proofs and focus on the case that a majority of verifiers are honest (i.e., \(t<n/2\)). We construct efficient MVZK protocols in the random oracle model where the prover sends one message to each verifier, while the verifiers only exchange one round of messages. When the threshold of corrupted verifiers \(t<n/2\), the prover sends \(1/2+o(1)\) field elements per multiplication gate to every verifier; when \(t<n(1/2-\epsilon )\) for some constant \(0<\epsilon <1/2\), we can further reduce the communication to O(1/n) field elements per multiplication gate per verifier. Our MVZK protocols demonstrate particularly high scalability: the proofs are streamable and only require a memory proportional to what is needed to evaluate the circuit in the clear.
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Acknowledgements
Work of Kang Yang is supported by the National Natural Science Foundation of China (Grant Nos. 62102037, 61932019). Work of Xiao Wang is supported in part by DARPA under Contract No. HR001120C0087, NSF award #2016240, and research awards from Meta, Google and PlatON Network. The views, opinions, and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.
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Yang, K., Wang, X. (2022). Non-interactive Zero-Knowledge Proofs to Multiple Verifiers. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13793. Springer, Cham. https://doi.org/10.1007/978-3-031-22969-5_18
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